- #1
OFFLINEX
- 7
- 0
Homework Statement
Factor 12X^3-12X^2-60X+24=0
OFFLINEX said:The Attempt at a Solution
How does factoring those terms help solve the equation? Boreck and Dunkle have already told him how to do this.Дьявол said:You could try something like this:
[tex]12(x^3-x^2-5x+2)=0[/tex]
[tex]12(x^3+2x^2-2x^2-x^2-4x-x+2)=0[/tex]
[tex]12([x^3+2x^2] - [2x^2+4x] - [x^2+x-2])=0[/tex]
Now factor the terms and solve the equation.
Regards.
Дьявол said:[tex]12[x^2(x+2)-2x(x+2)-(x+2)(x-1)]=0[/tex]
[tex]12(x+2)[x^2-2x-(x-1)]=0[/tex]
What I did is actually, I found that -2 is the solution of the polynomial, so I found out way to factor the whole polynomial and save some time for dividing the whole polynomial with (x+2).
Regards.
A 3rd degree polynomial is an algebraic expression that contains a variable raised to the power of 3, also known as a cubic polynomial. It follows the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.
Factoring is the process of finding the factors of a polynomial, which are expressions that can be multiplied together to get the original polynomial. In other words, factoring is reverse multiplication.
Factoring 3rd degree polynomials allows us to simplify complex expressions and solve equations. It can also help us find the roots, or solutions, of the polynomial equation.
To factor a 3rd degree polynomial, we use techniques such as grouping, common factor, and the quadratic formula. We can also use synthetic division or the rational root theorem if the polynomial is in standard form.
A prime polynomial is one that cannot be factored into simpler polynomials, while a composite polynomial can be factored into smaller polynomials. In other words, a prime polynomial has no factors other than 1 and itself, while a composite polynomial has multiple factors.